The on-loan striker is struggling with a calf injury which has limited the 31-year-old to just two appearances for the Hammers since he joined in January.
With the rest of his squad fit and in contention, manager Sam Allardyce will be tasked with picking the right team to end a run of four straight Premier League defeats.
Tottenham, meanwhile, will be without Andros Townsend after the winger underwent ankle surgery.
The 22-year-old damaged ankle ligaments at Stoke last weekend and went under the knife on Thursday, ruling him out for up to 10 weeks.
England team-mate Kyle Walker is also sidelined, as is Erik Lamela. Jan Vertonghen and Étienne Capoue are back training but unlikely to be involved.
A point should guarantee survival for West Ham, who are looking for a rare treble over Tottenham, having already beaten them in the league and cup at White Hart Lane.
Spurs needed a late Gareth Bale winner at Upton Park last season, and while Andy Carroll scored in that game, he has not scored at home for more than a year.
Only Liverpool have more away points than Tottenham, while only Newcastle and Norwich have taken fewer points than West Ham from the past eight games.
Stat of the game: West Ham gone 230 minutes since they last scored a goal in the Premier League.
West Ham (Possible, 4-4-1-1): Adrián; Demel, Tomkins, Reid, McCartney; Jarvis, Diamé, Noble, Downing; Nolan; Carroll.
Out: Borriello (calf).
Tottenham (Possible, 4-4-2): Lloris; Naughton, Dawson, Kaboul, Rose; Lennon, Chadli, Paulinho, Eriksen; Adebayor, Kane.
Out: Capoue (foot), Lamela (back), Soldado (hamstring), Townsend (ankle), Vertonghen (ankle), Walker (pelvis).
Referee: Phil Dowd. Matches: 25, R4 Y110.